Design and Evaluation of a Geometric Algebra-Based Graph Neural Network for Molecular Property Prediction

Kasper Helverskov Petersen, Mikkel N. Schmidt

Keywords: Geometric Algebra, Graph Neural Networks, Molecular Property Prediction, Message-passing Neural Networks, QM9, Geometric Algebra Graph Neural Network

Abstract: Geometric Algebra (GA) provides a unified framework for representing scalars, vectors, and higher-dimensional geometric elements, along with the geometric product, an operation that mixes information across these components in an equivariant manner. While GA has recently attracted attention in deep learning, its potential for molecular property prediction remains underexplored. We introduce GA-GNN, a novel equivariant graph neural network that extends message passing architectures from separate scalar and vector features to multivector representations, and employs sequences of geometric product layers as the core update mechanism. Evaluated on the QM9 benchmark, GA-GNN achieves competitive performance with the recent state-of-the-art while demonstrating that GA-based representations can simplify architecture design. These results highlight the potential of GA for building expressive equivariant message passing networks for molecular property prediction.

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Submission Number: 18